Least squares regression is a handy tool that helps us reduce mistakes when we make predictions. Here's a simple breakdown of how it works:

1. Measuring Errors: First, it looks at the differences between the actual values we see and the values we predicted. These differences are called residuals.

2. Focusing on Bigger Errors: Instead of just adding up the residuals, it squares them. This means it multiplies each difference by itself. This leads to the formula: $\text{Minimize} \sum (y_i - \hat{y}_i)^2$ Squaring the errors helps to make bigger mistakes count more than smaller ones.

3. Finding the Best Fit Line: The result is a line that best represents the data. This line helps us make better predictions.

In short, it’s all about finding the sweet spot where mistakes are as small as possible!